Moses became angry with the officers of the army: Those appointed over the army. [This comes] to teach you that when a generation is corrupt, the leaders are held responsible, for they have the power to protest. — [Sifrei Mattoth 43]

on Balaam’s advice: He said to them, "Even if you assemble all the multitudes of the world, you will not be able to overcome them. Are you more numerous than the Egyptians, who had six hundred chosen chariots? Come, and I will advise you. Their God hates immorality [thus, entice them to sin with your women…] as appears in [the chapter of] Cheilek (Sanh. 106a and in the Sifrei (Mattoth 43).

Every woman who can lie intimately with a man: Capable of sexual intercourse, even though she may never have experienced it. They passed them all in front of the showplate, and the faces of those capable of intercourse turned green. — [Yev. 60b]

you shall kill: Why is this repeated? In order to make a pause in the text; so says R. Ishmael. For when I read, “kill every male child, and every woman who can lie intimately with a man… And all the young girls…” I would not know whether to kill them [the women of the first verse] with the males, or allow them to live along with the young [girls]. That is why it says [at the end of the verse] “you shall kill.” - [Sifrei Mattoth 45]

outside the camp: [This means] that they should not enter the courtyard [of the Mishkan].

מחוץ למחנה: שלא יכנסו לעזרה:

anyone who killed a person: R. Meir says, Scripture speaks of one who killed with a weapon susceptible to contamination, and it teaches that a vessel defiles a person when it is in contact with a corpse, as if he were actually in contact with the corpse itself. Or, I might think that [he becomes contaminated] even if he shot an arrow and killed him. Scripture therefore teaches, “or who touched a corpse,” equating the one who kills with the one who touches. Just as one who touches is [contaminated] through contact, so is the one who kills [contaminated] through contact. — [Sifrei Chukkath 48]

shall cleanse himself: with sprinkling water, as is the law with others who were defiled through contact with corpses. For even those who believe that gentile graves do notcontaminate [an Israelite] if they are under the same roof-as it says, “You my sheep, the sheep of My pasture; you are men” (Ezek.. 34:31) [and the Sages add,] only you are called “men” (Yev. 61a)-admit that gentiles contaminate through contact and carrying, for [the term] “men” is said only in reference to uncleanness caused by being in the same tent [namely, under one roof] as it says,“[This is the law for a man (אָדָם) who dies in a tent” (19:14).

you and your captives: Not that gentiles are susceptible to contamination and therefore require sprinkling, but just as you are members of the covenant, so too your captives, should they become contaminated after they enter the covenant [of God], they require sprinkling. — [Sifrei Mattoth 46]

Eleazar the kohen…: Since Moses came to a state of anger, he came to err, for the laws of purging gentile vessels eluded him. A similar incident happened on the eighth day of the investitures [of the kohanim], as it says, “He [Moses] became angry with Eleazar and Ithamar” (Lev. 10: 16); he came to a state of anger, so he came to err. Similarly, in the episode of“Now listen, you rebels… and struck the rock” (20:10-11); through anger, he came to err. — [Sifrei Mattoth 48]

Only the gold etc.: Even though Moses warned you only about the laws of ritual uncleanness, you must further be warned of the laws concerning the purging [of contaminated vessels]. [The word] אַךְ “only” is an exclusive expression, that is to say, you are excluded from using vessels even after their purification from contamination by a corpse, until they have been purged from the absorption of the forbidden flesh of carrion. Our Rabbis said,“ Only the gold…” teaches you that one must remove its rust before one purges it. This is the meaning of אַךְ “only”-there should be no rust; “only” the metal itself in its original form. — [Targum Jonathan ben Uzziel, Yalkut Shimoni]

23whatever is used in fire you shall pass through fire and then it will be clean; it must, however, [also] be cleansed with sprinkling water, and whatever is not used in fire you shall pass through water.

shall pass through fire: It is purged in the manner it is used. If it is used in hot water, it must be purged in hot water, and if it is used for roasting, such as a spit or grill, it must be made to glow in fire. — [A.Z. 75b]

it must, however, [also] be cleansed with sprinkling water: According to its simple meaning, this sprinkling was to cleanse it from contamination by a corpse. He said to them,“The vessels require purging to cleanse them from the [absorption of] forbidden [food], and sprinkling to cleanse them of [spiritual] uncleanness [caused by a corpse].” Our Rabbis expounded from here that even to make them fit for use [after contamination] from forbidden food, ritual immersion was required for metal utensils. They expound מֵי נִדָּה written here to mean water fit for a menstruant [Heb. נִדָּה] to immerse herself in. How much is that? Forty 'seah.’- [A.Z. 75b]